"""simple docstring"""


import logging

import numpy as np
import pytest
from scipy.linalg import eigh

logging.basicConfig(level=logging.INFO, format='%(message)s')





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   np.ndarray:




						'''simple docstring'''



						return input_array.reshape((input_array.size, 1)							)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   np.ndarray:




						'''simple docstring'''



						lowerCamelCase__   =np.nan
						for i in range(__lowerCAmelCase							):
												lowerCamelCase__   =features[:, labels == i]
												lowerCamelCase__   =data.mean(1							)
												# Centralize the data of class i
												lowerCamelCase__   =data - column_reshape(__lowerCAmelCase							)
												if i > 0:
																		# If covariance_sum is not None
																		covariance_sum += np.dot(__lowerCAmelCase  ,       centered_data.T							)
												else:
																		# If covariance_sum is np.nan (i.e. first loop)
																		lowerCamelCase__   =np.dot(__lowerCAmelCase  ,       centered_data.T							)

						return covariance_sum / features.shape[1]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   np.ndarray:




						'''simple docstring'''



						lowerCamelCase__   =features.mean(1							)
						lowerCamelCase__   =np.nan
						for i in range(__lowerCAmelCase							):
												lowerCamelCase__   =features[:, labels == i]
												lowerCamelCase__   =data.shape[1]
												lowerCamelCase__   =data.mean(1							)
												if i > 0:
																		# If covariance_sum is not None
																		covariance_sum += device_data * np.dot(
																		    column_reshape(__lowerCAmelCase							) - column_reshape(__lowerCAmelCase							)  ,       (column_reshape(__lowerCAmelCase							) - column_reshape(__lowerCAmelCase							)).T  ,       )
												else:
																		# If covariance_sum is np.nan (i.e. first loop)
																		lowerCamelCase__   =device_data * np.dot(
																		    column_reshape(__lowerCAmelCase							) - column_reshape(__lowerCAmelCase							)  ,       (column_reshape(__lowerCAmelCase							) - column_reshape(__lowerCAmelCase							)).T  ,       )

						return covariance_sum / features.shape[1]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   np.ndarray:




						'''simple docstring'''



						if features.any():
												lowerCamelCase__   =features.mean(1							)
												# Center the dataset
												lowerCamelCase__   =features - np.reshape(__lowerCAmelCase  ,       (data_mean.size, 1)							)
												lowerCamelCase__   =np.dot(__lowerCAmelCase  ,       centered_data.T							) / features.shape[1]
												lowerCamelCase__   , lowerCamelCase__   =np.linalg.eigh(__lowerCAmelCase							)
												# Take all the columns in the reverse order (-1), and then takes only the first
												lowerCamelCase__   =eigenvectors[:, ::-1][:, 0:dimensions]
												# Project the database on the new space
												lowerCamelCase__   =np.dot(filtered_eigenvectors.T  ,       __lowerCAmelCase							)
												logging.info("Principal Component Analysis computed"							)

												return projected_data
						else:
												logging.basicConfig(level=logging.ERROR  ,       format="%(message)s"  ,       force=__lowerCAmelCase							)
												logging.error("Dataset empty"							)
												raise AssertionError





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   np.ndarray:




						'''simple docstring'''



						assert classes > dimensions

						# Check if features have been already loaded
						if features.any:
												lowerCamelCase__   , lowerCamelCase__   =eigh(
												    covariance_between_classes(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)  ,       covariance_within_classes(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)  ,       )
												lowerCamelCase__   =eigenvectors[:, ::-1][:, :dimensions]
												lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =np.linalg.svd(__lowerCAmelCase							)
												lowerCamelCase__   =svd_matrix[:, 0:dimensions]
												lowerCamelCase__   =np.dot(filtered_svd_matrix.T  ,       __lowerCAmelCase							)
												logging.info("Linear Discriminant Analysis computed"							)

												return projected_data
						else:
												logging.basicConfig(level=logging.ERROR  ,       format="%(message)s"  ,       force=__lowerCAmelCase							)
												logging.error("Dataset empty"							)
												raise AssertionError





def      lowerCamelCase_					(   )				->   None:




						'''simple docstring'''



						lowerCamelCase__   =np.array([[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7]]							)
						lowerCamelCase__   =np.array([0, 0, 0, 1, 1]							)
						lowerCamelCase__   =2
						lowerCamelCase__   =2

						# Assert that the function raises an AssertionError if dimensions > classes
						with pytest.raises(__lowerCAmelCase							) as error_info:
												lowerCamelCase__   =linear_discriminant_analysis(
												    __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
												if isinstance(__lowerCAmelCase  ,       np.ndarray							):
																		raise AssertionError(
																		    "Did not raise AssertionError for dimensions > classes"							)
												assert error_info.type is AssertionError





def      lowerCamelCase_					(   )				->   None:




						'''simple docstring'''



						lowerCamelCase__   =np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]							)
						lowerCamelCase__   =2
						lowerCamelCase__   =np.array([[6.9282_0323, 8.6602_5404, 10.3923_0485], [3.0, 3.0, 3.0]]							)

						with pytest.raises(__lowerCAmelCase							) as error_info:
												lowerCamelCase__   =principal_component_analysis(__lowerCAmelCase  ,       __lowerCAmelCase							)
												if not np.allclose(__lowerCAmelCase  ,       __lowerCAmelCase							):
																		raise AssertionError
												assert error_info.type is AssertionError


if __name__ == "__main__":
	import doctest

	doctest.testmod()



"""simple docstring"""


from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   List[Any]:




						'''simple docstring'''



						def is_in_circle(__lowerCAmelCase  ,       __lowerCAmelCase							) -> bool:
												lowerCamelCase__   =sqrt((x**2) + (y**2)							)
												# Our circle has a radius of 1, so a distance
												# greater than 1 would land outside the circle.
												return distance_from_centre <= 1

						# The proportion of guesses that landed in the circle
						lowerCamelCase__   =mean(
						    int(is_in_circle(uniform(-1.0  ,       1.0							)  ,       uniform(-1.0  ,       1.0							)							)							)
						    for _ in range(__lowerCAmelCase							)							)
						# The ratio of the area for circle to square is pi/4.
						lowerCamelCase__   =proportion * 4
						print(F'''The estimated value of pi is {pi_estimate}'''							)
						print(F'''The numpy value of pi is {pi}'''							)
						print(F'''The total error is {abs(pi - pi_estimate							)}'''							)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase = 0.0  ,       __lowerCAmelCase = 1.0  ,       )				->   float:




						'''simple docstring'''



						return mean(
						    function_to_integrate(uniform(__lowerCAmelCase  ,       __lowerCAmelCase							)							) for _ in range(__lowerCAmelCase							)							) * (max_value - min_value)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase = 0.0  ,       __lowerCAmelCase = 1.0							)				->   None:




						'''simple docstring'''



						def identity_function(__lowerCAmelCase							) -> float:
												return x

						lowerCamelCase__   =area_under_curve_estimator(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =(max_value * max_value - min_value * min_value) / 2

						print("******************"							)
						print(F'''Estimating area under y=x where x varies from {min_value} to {max_value}'''							)
						print(F'''Estimated value is {estimated_value}'''							)
						print(F'''Expected value is {expected_value}'''							)
						print(F'''Total error is {abs(estimated_value - expected_value							)}'''							)
						print("******************"							)





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   None:




						'''simple docstring'''



						def function_to_integrate(__lowerCAmelCase							) -> float:
												return sqrt(4.0 - x * x							)

						lowerCamelCase__   =area_under_curve_estimator(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       0.0  ,       2.0							)

						print("******************"							)
						print("Estimating pi using area_under_curve_estimator"							)
						print(F'''Estimated value is {estimated_value}'''							)
						print(F'''Expected value is {pi}'''							)
						print(F'''Total error is {abs(estimated_value - pi							)}'''							)
						print("******************"							)


if __name__ == "__main__":
	import doctest

	doctest.testmod()


